Veröffentlichungen

Bücher

• B. Hofmann, A. Leitao, J.P. Zubelli (Eds.):
  New Trends in Parameter Identification for Mathematical Models.
  Birkhäuser,Trends in Mathematics,
  Springer International Publishing, Cham, Switzerland 2018,
  ISBN 978-3-319-70823-2, ISBN 978-3-319-70824-9 (eBook)
• T. Schuster, B. Kaltenbacher, B. Hofmann, K.S. Kazimierski:
  Regularization Methods in Banach Spaces.
  Walter de Gruyter GmbH & Co. KG,
  Reihe: Radon Series on Computational and Applied Mathematics 10,
  Berlin/Boston 2012, ISBN 978-3-11-025524-9.
• B. Hofmann:
  Mathematik inverser Probleme.
  B.G. Teubner Stuttgart-Leipzig, Leipzig 1999.
  ISBN 978-3-519-00254-3. Fulltext download
• B. Hofmann:
  Regularization for Applied Inverse and Ill-Posed Problems.
  B.G. Teubner Leipzig, Teubner-Texte zur Mathematik, Bd. 85, Leipzig 1986.
  Reprint Vieweg/Springer 2013 ISBN 978-3-322-93035-4.
  E-Book ISBN 978-3-322-93034-7.

Ausgewählte Publikationen

Siehe auch Veröffentlichungen im Volltext

• P. Mathé, B. Hofmann:
  Tractability of linear ill-posed problems in Hilbert space.
  Journal of Complexity 84 (2024), 101867,
  https://doi.org/10.1016/j.jco.2024.101867.
• S. Kindermann, B. Hofmann:
  Curious ill-posedness phenomena in the composition of non-compact linear operators in Hilbert spaces.
  Journal Inverse and Ill-Posed Problems 24 (2024), Number 5, 1001-1013,
  https://doi.org/10.1515/jiip-2024-0007.
• B. Hofmann, H.-J. Fischer:
  A note on the degree of ill-posedness for mixed differentiation on the d-dimensional unit cube.
  Journal Inverse and Ill-Posed Problems 23 (2023), Number 6, 949-957,
  DOI: 10.1515/jiip-2023-0025.
• O. Scherzer, B. Hofmann, Z. Nashed:
  Gauss-Newton method for solving linear inverse problems with neural network coders.
  Sampling theory, signal processing, and data analysis 21 (2023), Number 2, Article 25,
  DOI: 10.1007/s43670-023-00066-6.
• B. Hofmann, F. Werner, Y. Deng:
  On uniqueness and ill-posedness for the deautoconvolution problem in the multi-dimensional case.
  Inverse Problems 39 (2023), Number 6, 065012 (15pp),
  DOI: 10.1088/1361-6420/acd07b.
• B. Hofmann, C. Klinkhammer, R. Plato:
  New results for variational regularization with oversmoothing penalty term in Banach spaces.
  Communications on Analysis and Computation 1, Issue 2 (2023), 94-115,
  DOI: 10.3934/cac.2023006.
• Y. Deng, B. Hofmann, F. Werner:
  Deautoconvolution in the two-dimensional case.
  Electronic Transactions on Numerical Analysis 59 (2023), 24-42,
  DOI: 10.1553/etna vol59s24.
• B. Hofmann, P. Mathé:
  The degree of ill-posedness of composite linear ill-posed problems with focus on the impact
  of the non-compact Hausdorff moment operator.
  Electronic Transactions on Numerical Analysis 57 (2022), 1-16.
  DOI: 10.1553/etna vol57s1.
• B. Hofmann, C. Hofmann, P. Mathé, R. Plato:
  Nonlinear Tikhonov regularization in Hilbert scales with oversmoothing penalty: inspecting balancing principles.
  Chapter 4 in: Deterministic and Stochastic Optimal Control and Inverse Problems (Eds.: B. Jadamba, A. A. Khan,
  S. Migorski, M. Sama). CRC Press (Taylor & Francis Group), Boca Raton 2022, pp. 79-111.
  ISBN 978-0-367-50630-8 (hbk), ISBN 978-0-367-50631-5 (pbk), ISBN 978-1-003-05057-5 (ebk),
  DOI: 10.1201/9781003050575.
• P. Mathé, M.T. Nair, B. Hofmann:
  Regularization of linear ill-posed problems involving multiplication operators.
  Applicable Analysis 101, Issue 2 (2022), 714-732,
  DOI: 10.1080/00036811.2020.1758308.
• D. Gerth, B. Hofmann:
  A note on open questions asked to analysis and numerics concerning the Hausdorff moment problem.
  Eurasian Journal of Mathematical and Computer Applications 10, Issue 1 (2022), 40-50.
• D. Chen, B. Hofmann, I. Yousept:
  Oversmoothing Tikhonov regularization in Banach spaces.
  Inverse Problems 37 (2021), 085007 (28pp).
• D. Gerth, B. Hofmann, C. Hofmann, S. Kindermann:
  The Hausdorff moment problem in the light of ill-posedness of type I.
  Eurasian Journal of Mathematical and Computer Applications 9, Issue 2 (2021), 57-87.
• Y. Zhang, B. Hofmann:
  Two new non-negativity preserving iterative regularization methods for ill-posed inverse problems.
  Inverse Problems and Imaging 15 (2021), 229-256.
• B. Hofmann, R.Plato:
  Convergence results and low order rates for nonlinear Tikhonov regularization with oversmoothing penalty term.
  Electronic Transactions on Numerical Analysis 53 (2020), 313-328.
• F. Werner, B. Hofmann:
  Convergence analysis of (statistical) inverse problems under conditional stability estimates.
  Inverse Problems 36 (2020), 015004 (23pp).
• Y. Zhang, B. Hofmann:
  On the second-order asymptotical regularization of linear ill-posed problems.
  Applicable Analysis 99 (2020), 1000-1025.
• B. Hofmann, C. Hofmann:
  The impact of the discrepancy principle on the Tikhonov-regularized solutions with oversmoothing penalties.
  Mathematics (www.mdpi.com) 8 (2020), 331 (16pp).
• B. Hofmann, P. Mathé:
  A priori parameter choice in Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems.
  Chapter 8 in: Inverse Problems and Related Topics: Shanghai, China, October 12-14, 2018
  (Eds.: J. Cheng, S. Lu, M. Yamamoto). Book 310 of Springer Proceedings in Mathematics & Statistics. Springer Nature, Singapore 2020 (ISBN 978-981-15-1591-0. ISBN 978-981-15-1592-7 (eBook)), pp. 169-176.
• D. Gerth, B. Hofmann, C. Hofmann:
  Case studies and a pitfall for nonlinear variational regularization under conditional stability.
  Chapter 9 in: Inverse Problems and Related Topics: Shanghai, China, October 12-14, 2018
  (Eds.: J. Cheng, S. Lu, M. Yamamoto). Book 310 of Springer Proceedings in Mathematics & Statistics. Springer Nature, Singapore 2020 (ISBN 978-981-15-1591-0. ISBN 978-981-15-1592-7 (eBook)), pp. 177-203.
• R. Gong, B. Hofmann, Y. Zhang:
  A new class of accelerated regularization methods, with application to bioluminescence tomography.
  Inverse Problems 36 (2020), 055013 (36pp).
• R. Ramlau, C. Koutschan, B. Hofmann:
  On the singular value decomposition of n-fold integration operators.
  Chapter 11 in: Inverse Problems and Related Topics: Shanghai, China, October 12-14, 2018
  (Eds.: J. Cheng, S. Lu, M. Yamamoto). Book 310 of Springer Proceedings in Mathematics & Statistics. Springer Nature, Singapore 2020 (ISBN 978-981-15-1591-0. ISBN 978-981-15-1592-7 (eBook)), pp. 237-256.
• Y. Zhang, B. Hofmann:
  On Fractional asymptotical regularization of linear ill-posed problems in Hilbert spaces.
  Fractional Calculus and Applied Analysis 22 (2019), 699-721.
• E. Escoto, D. Gerth, B. Hofmann, G. Steinmeyer:
  Strategies for the characterization of partially coherent ultrashort pulses with dispersion scan.
  Journal of the Optical Society of America B 36 (2019), 2092-2098.
• R. Plato, B. Hofmann:
  A regularized variational inequality approach for nonlinear monotone ill-posed problems.
  Journal of Optimization Theory 182 (2019), 525-539.
• W. Wang, S. Lu, B. Hofmann, J. Cheng:
  Tikhonov regularization with l0-term complementing a convex penalty: l1-convergence under sparsity constraints.
  Journal of Inverse and Ill-posed Problems 27 (2019), 575-590.
• D. Gerth, B. Hofmann:
  Oversmoothing regularization with l1-penalty term.
  AIMS Mathematics 4 (2019), 1223-1247.
• C. Hofmann, B. Hofmann, A. Pichler:
  Simultaneous identification of volatility and interest rate functions -- a two parameter regularization approach.
  Electronic Transactions on Numerical Analysis 51 (2019), 99-117.
• M. Hinze, B. Hofmann, Tran Nhan Tam Quyen:
  A regularization approach for an inverse source problem in elliüptic systems from single Cauchy data.
  Numerical Functional Analysis and Optimization 40 (2019), 1080-1112.
• B. Hofmann, S. Kindermann, P. Mathé:
  Penalty-based smoothness conditions in convex variational regularization.
  Journal of Inverse and Ill-posed Problems 27 (2019), 283-300.
• D. Gerth, E. Escoto, G. Steinmeyer, B. Hofmann:
  Regularized differential evolution for a blind phase retrieval problem in ultrashort laser pulse characteriztaion.
  Review of Scientific Instruments 90 (2019), 043116.
• H. Egger, B. Hofmann:
  Tikhonov regularization in Hilbert scales under conditional stability assumptions.
  Inverse Problems 34 (2018),115015 (17pp).
• B. Hofmann, R. Plato:
  On ill-posedness concepts, stable solvability and saturation
  Journal of Inverse and Ill-posed Problems 26 (2018), 287-297.
• D. Chen, B. Hofmann, J. Zou:
  Regularization and convergence for ill-posed backward evolution equations in Banach spaces.
  J. Differential Equations 265 (2018), 3533-3566.
• J. Flemming, D. Gerth:
  Injectivity and weak*-to-weak continuity suffice for convergence rates in l^¹-regularization.
  Journal of Inverse and Ill-posed Problems 26 (2018), 85-94.
• R. Plato, P. Mathé, B. Hofmann:
  Optimal rates for Lavrentiev regularization with adjoint source conditions.
  Mathematics of Computation 87 (2018), 785-801.
• B. Hofmann, P. Mathé:
  Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales.
  Inverse Problems 34 (2018), 015007 (14pp).
• D. Gerth:
  Convergence rates for l1-regularization without the help of a variational inequality.
  Electronic Transactions on Numerical Analysis 47 (2017), 233-244.
• D. Gerth, A. Hofinger, R. Ramlau:
  On the lifting of deterministic convergence rates for inverse problems with stochastic noise.
  Inverse Problems and Imaging 11 (2017), 663 - 687.
• S. Bürger, P. Mathé:
  Discretized Lavrent'ev regularization for the autoconvolution equation.
  Applicable Analysis 96 (2017), 1618-1637.
• D. Chen, B. Hofmann, J. Zou:
  Elastic-net regularization versus l1-regularization for linear inverse problems with quasi-sparse solutions.
  Inverse Problems 33 (2017), 015004 (17pp).
• R. Bot, B. Hofmann:
  Conditional stability versus ill-posedness for operator equations with monotone operators in Hilbert space.
  Inverse Problems 32 (2016), 125003 (23pp).
• B. Hofmann, B. Kaltenbacher, E. Resmerita:
  Lavrentiev's regularization method in Hilbert spaces revisited.
  Inverse Problems and Imaging 10 (2016), 741-764.
• S. Bürger, J. Flemming, B. Hofmann:
  On complex-valued deautoconvolution of compactly supported functions with sparse Fourier representation.
  Inverse Problems 32 (2016), 104006 (12pp).
• J. Flemming:
  Convergence rates for l¹-regularization without injectivity-type assumptions.
  Inverse Problems 32 (2016), 095001 (19pp).
• J. Flemming, B. Hofmann, I. Veselic:
  A unified approach to convergence rates for l1-regularization and lacking sparsity.
  Journal of Inverse and Ill-posed Problems 24 (2016), 139-148.
• S.W. Anzengruber, S. Bürger, B. Hofmann, G.Steinmeyer:
  Variational regularization of complex deautoconvolution and phase retrieval in ultrashort laser pulse characterization.
  Inverse Problems 32, No.3 (2016), 035002 (27pp).
• J. Flemming, B. Hofmann, I. Veselic:
  On l1- regularization in light of Nashed's ill-posedness concept.
  Computational Methods in Applied Mathematics 15 (2015), 279-289.
• S. Bürger, J. Flemming:
  Deautoconvolution: A new decomposition approach versus TIGRA and local regularization.
  Journal of Inverse and Ill-posed Problems 23 (2015), 231-243.
• B. Hofmann:
  On smoothness concepts in regularization for nonlinear inverse problems in Banach spaces.
  Chapter~8 in Mathematical and Computational Modeling: With Applications in Natural and Social Sciences,
  Engineering, and the Arts (Ed.: R.~Melnik).
  John Wiley, New Jersey 2015, pp.~192--221. ISBN 978-1-118-85398-6.
• S. Birkholz, G. Steinmeyer, S. Koke, D. Gerth, S. Bürger, B. Hofmann:
  Phase retrieval via regularization in self-diffraction-based spectral interferometry.
  Journal of the Optical Society of America B 32, No.5 (2015), 983-992.
• S. Bürger, B. Hofmann:
  About a deficit in low-order convergence rates on the example of autoconvolution.
  Applicable Analysis 94, No.3 (2015), 477-493.
• S.W. Anzengruber, B. Hofmann, P. Mathé:
  Regularization properties of the sequential discrepancy principle for Tikhonov regularization in Banach spaces.
  Applicable Analysis 93, No.7 (2014), 1382-1499.
• J. Cheng, B. Hofmann, S. Lu:
  The index function and Tikhonov regularization for ill-posed problems.
  Journal of Computational and Applied Mathematics 265 (2014), 110-119.
• D. Gerth, B. Hofmann, S. Birkholz, S. Koke, G. Steinmeyer:
  Regularization of an autoconvolution problem in ultrashort laser pulse characterization.
  Inverse Problems in Science and Engineering 22, No.2 (2014), 245-266.
• J. Flemming:
  Regularization of autoconvolution and other ill-posed quadratic equations by decomposition.
  Journal of Inverse and Ill-posed Problems 22 (2014), 551-567.
• S.W. Anzengruber, B. Hofmann, R.Ramlau:
  On the interplay of basis smoothness and specific range conditions occurring in sparsity regularization.
  Inverse Problems 29 (2013), 125002 (21pp).
• U.Tautenhahn, U.Hämarik, B. Hofmann, Y.Shao:
  Conditional stability estimates for ill-posed PDE problems by using interpolation.
  Numerical Functional Analysis and Optimization 34 (2013), 1370-1417.
• M. Burger, J. Flemming, B.Hofmann:
  Convergence rates in l1-regularization if the sparsity assumption fails.
  Inverse Problems 29 (2013), 025013 (16pp).
• R. Bot, B. Hofmann:
  The impact of a curious type of smoothness conditions on convergence rates in l1-regularization.
  Eurasian Journal of Mathematical and Computer Applications 1, No.1 (2013), 29-40.
• R. Bot, B. Hofmann, P. Mathé:
  Regularizability of ill-posed problems and the modulus of continuity.
  Zeitschrift f. Analysis und ihre Anwendungen 32, No.3 (2013), 299-312.
• J. Flemming:
  Variational smoothness assumptions in convergence rate theory - an overview.
  Journal of Inverse and Ill-posed Problems 21 (2013), 395-409.
• S. Lu, J. Flemming:
  Convergence rate analysis of Tikhonov regularization for nonlinear ill-posed problems with noisy operators.
  Inverse Problems 28 (2012), 104003 (20 pp).
• J. Flemming:
  Solution smoothness of ill-posed equations in Hilbert spaces: four concepts and their cross connections.
  Applicable Analysis 91 (2012), 1029-1044.
• B. Hofmann, P. Mathé:
  Parameter choice in Banach space regularization under variational inequalities.
  Inverse Problems 28 (2012), 104006 (17pp).
• B. Hofmann, P. Mathé:
  A note on the modulus of continuity for ill-posed problems in Hilbert space.
  Trudy Inst. Mat. i Mekh. UrO RAN 18, No.1 (2012), 34-41.
• J. Flemming, B.Hofmann:
  Convergence rates in constrained Tikhonov regularization: equivalence of projected source conditions and variational inequalities.
  Inverse Problems 27 (2011), 085001 (11pp).
• M. Hegland, B. Hofmann:
  Errors of regularisation under range inclusions using variable Hilbert scales.
  Inverse Problems and Imaging 5 (2011), 619-643.
• J. Flemming, B.Hofmann, P.Mathé:
  Sharp converse results for the regularization error using distance functions.
  Inverse Problems 27 (2011), 025006 (18pp).
• J. Flemming:
  Theory and examples of variational regularization with non-metric fitting functionals.
  Journal of Inverse and Ill-posed Problems 18 (2010), 677-699.
• B. Hofmann, S. Kindermann:
  On the degree of ill-posedness for linear problems with non-compact operators.
  Methods and Applications of Analysis 17 (2010), 445-461.
• R.I.Bot, B.Hofmann:
  An extension of the variational approach for obtaining convergence rates in regularization of nonlinear ill-posed problems.
  Journal of Integral Equations and Applications 22 (2010), 369-392.
• B.Hofmann, M.Yamamoto:
  On the interplay of source conditions and variational inequalities for nonlinear ill-posed problems.
  Applicable Analysis 89 (2010), 1705-1727.
• A.Neubauer, T.Hein, B.Hofmann, S.Kindermann, U.Tautenhahn:
  Improved and extended results for enhanced convergence rates of Tikhonov regularization in Banach spaces.
  Applicable Analysis 89 (2010), 1729-1743.
• J. Flemming, B.Hofmann:
  A new approach to source conditions in regularization with general residual term.
  Numer. Funct. Anal. Optimiz. 31 (2010), 254-284.
• S.V. Pereverzev, B.Hofmann:
  Estimation of linear functionals from indirect noisy data without knowledge of the noise level.
  GEM - International Journal on Geomathematics 1 (2010), 121-131.
• B. Kaltenbacher, B.Hofmann:
  Convergence rates for the iteratively regularized Gauss-Newton method in Banach spaces.
  Inverse Problems 26 (2010), 035007 (21pp).
• B.Hofmann, P.Mathé, H.von Weizsäcker:
  Regularization in Hilbert space under unbounded operators and general source conditions.
  Inverse Problems 25 (2009), 115013 (15pp).
• T.Hein, B.Hofmann:
  Approximate source conditions for nonlinear ill-posed problems -- chances and limitations.
  Inverse Problems 25 (2009), 035003 (16pp).
• B.Hofmann, L.von Wolfersdorf:
  A new result on the singular value asymptotics of integration operators with weights.
  Journal of Integral Equations and Applications 21 (2009), 281-295.
• B.Hofmann, P.Mathé, M.Schieck:
  Modulus of continuity for conditionally stable ill-posed problems in Hilbert space.
  J. Inv. Ill-posed Problems 16 (2008), 567-585.
• P.Mathé, B.Hofmann:
  How general are general source conditions?
  Inverse Problems 24 (2008), 015009 (5pp).
• P.Mathé, B.Hofmann:
  Direct and inverse results in variable Hilbert scales.
  Journal of Approximation Theory 154 (2008), 77-89.
• L. von Wolfersdorf, B.Hofmann:
  A specific inverse problem for the Volterra convolution equation.
  Applicable Analysis 87 (2008), 59-81.
• B.Hofmann, P.Mathé, S.V.Pereverzev:
  Regularization by projection: Approximation theoretic aspects and distance functions.
  J. Inverse and Ill-Posed Problems 15 (2007), 527-545.
• B. Hofmann, P.Mathé:
  Analysis of profile functions for general linear regularization methods
  SIAM J. Numer. Anal. 45 (2007), 1122-1141.
• B. Hofmann, B. Kaltenbacher, C. Pöschl, O. Scherzer:
  A convergence rates result in Banach spaces with non-smooth operators
  Inverse Problems 23 (2007), 987-1010.
• B. Hofmann, M. Schieck, L. von Wolfersdorf:
  On the analysis of distance functions for linear ill-posed problems with an application to the integration operator in L^2
  J. Inv. Ill-Posed Problems 15 (2007), 83-98.
• D. Düvelmeyer, B. Hofmann, M. Yamamoto:
  Range inclusions and approximate source conditions with general benchmark functions
  Numerical Functional Analysis and Optimization 28 (2007), 1245-1261.
• T. Hein, B. Hofmann, A. Meyer, P.Steinhorst:
  Numerical analysis of a calibration problem for simulating electric fault arc tests
  Inverse Problems in Science and Engineering 15 (2007), 679-698.
• D. Düvelmeyer, B. Hofmann:
  A multi-parameter regularization approach for estimating parameters in jump diffusion processes
  J. Inv. Ill-Posed Problems 14 (2006), 861-880.
• B. Hofmann:
  Approximate source conditions in Tikhonov-Phillips regularization and consequences for inverse problems with multiplication operators
  Mathematical Methods in the Applied Sciences 29 (2006), 351-371.
• A. Böttcher, B. Hofmann, U. Tautenhahn, M. Yamamoto:
  Convergence rates for Tikhonov regularization from different kinds of smoothness conditions
  Applicable Analysis 85 (2006), 555-578.
• H. Egger, T. Hein, B. Hofmann:
  On decoupling of volatility smile and term structure in inverse option pricing
  Inverse Problems 22 (2006), 1247-1259.
• B. Hofmann, D. Düvelmeyer, K. Krumbiegel:
  Approximate source conditions in Tikhonov regularization - new analytical results and some numerical studies
  Mathematical Modelling and Analysis 11 (2006), 41-56.
• B. Hofmann, L. von Wolfersdorf:
  On the determination of a density function by its autoconvolution coefficient
  Numerical Functional Analysis and Optimization 27 (2006), 357-375.
• B. Hofmann, M. Yamamoto:
  Convergence rates for Tikhonov regularization based on range inclusions
  Inverse Problems 21 (2005), 850-820.
• M. Freitag, B. Hofmann:
  Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems
  J. Inverse and Ill-Posed Problems 13 (2005), 123-148.
• B. Hofmann, R. Krämer:
  On maximum entropy regularization for a specific inverse problem of option pricing
  J. Inverse and Ill-Posed Problems 13 (2005), 41-63.
• B. Hofmann, L. v. Wolfersdorf:
  Some results and a conjecture on the degree of ill-posedness for integration operators with weights
  Inverse Problems 21 (2005), 427-433.
• P. Steinhorst, B. Hofmann, A. Meyer, W. Weinelt:
  Gas temperature identification for the simulation of electric fault arc tests
  Proceedings of 5th International Conference on Inverse Problems in Engineering: Theory and Practice, Cambridge July 2005, Volume III (Ed.: D. Lesnic), Leeds University Press, Leeds UK 2005, S12/1-8.
• D. Düvelmeyer, B. Hofmann:
  Ill-posedness of parameter estimation in jump diffusion processes
  Tagungsband zum Workshop Stochastische Analysis
  Bärenstein 2004 (Hrsg.: J. vom Scheidt), TU Chemnitz, 5-20.
• T. Hein, B. Hofmann:
  On the nature of ill-posedness of an inverse problem arising in option pricing
  Inverse Problems 19 (2003), 1319-1338.
• B. Hofmann, F. Thießen, V. Weber, R. Wunderlich:
  Vermögensaufteilung für die Altersvorsorge: Wie fundiert sind langfristige Allokationsregeln?
  Zeitschrift für Bankrecht und Bankwirtschaft (ZBB) 15 (2003), 261-276.
• S. Pohl, B. Hofmann, R. Neubert, T. Otto, C. Radehaus:
  A regularization approach for the determination of remission curves.
  Inverse Problems in Engineering 9 (2001), 157-174.
• B. Hofmann, G. Fleischer:
  Stability rates for linear ill-posed problems with compact and non-compact operators.
  Z. Anal. Anwendungen 18 (1999), 267-286.
• B. Hofmann, O. Scherzer:
  Local ill-posedness and source conditions of operator equations in Hilbert spaces.
  Inverse Problems 14 (1998), 1189-1206.
• B. Hofmann, U. Tautenhahn:
  On ill-posedness measures and space change in Sobolev scales.
  Z. Anal. Anwendungen 16 (1997), 979-1000.
• B. Hofmann:
  On the degree of ill-posedness for nonlinear problems.
  J. Inv. Ill-Posed Problems 2 (1994), 61-76.